No, there is no such legal requirement (unless you are applying for H1-B immigration status or something). The employer is only required to pay you minimum wage under California law.
The information presented here is general in nature and is not intended, nor should be construed, as legal advice. This posting does not create any attorney-client relationship with the author (who is only admitted to practice law in the State of California). For specific advice about your particular situation, consult your own attorney.